4 papers
Two associative operads of packed words
Samuele Giraudo, Yannic Vargas
The associative operad is a central structure in operad theory, defined on the linear span of the set of permutations. We build two analogs of the associative operad on the linear…
On the free commutative monoid over a positive operad
Dominique Manchon, Hedi Regeiba, Imen Rjaiba +1
We study algebraic structures on the free commutative twisted algebra generated by a positive operad , in the framework of vector species. Given a nonunital commutative…
Antipode formulas for pattern Hopf algebras
Raúl Penaguiao, Yannic Vargas
The permutation pattern Hopf algebra is a commutative filtered and connected Hopf algebra. Its product structure stems from counting patterns of a permutation, interpreting the coe…
Hopf algebras of parking functions and decorated planar trees
Nantel Bergeron, Rafael S. González D'León, Shu Xiao Li +2
We construct three new combinatorial Hopf algebras based on the Loday-Ronco operations on planar binary trees. The first and second algebras are defined on planar trees and labeled…